Hierarchical Logistic regression
Rick Handel
I'm a newbie to logistic regression and I have a few questions for a study
that I'm working on. Any input would be greatly appreciated!
Normally I've run analyses for hierarchical regression with a continuous
dependent variable like this:
Note - v1, v2, and group are continuous; v3 is a dichotomous dummy variable
regression variables = v1 v2 v3 group
/dependent=group
/method=enter v1 v2
/method = enter v3.
execute.
I've assessed the incremental contribution of v3 by investigating the F
change and significance of F change and reporting the extra variance
accounted for (R-squared change).
Now I'm working on an analysis where v1 and v2 are continuous, v3 is a
dichotomous dummy variable, and group is a dichotomous variable. First, I'd
like to check if my syntax is correct for a hierarchical logistic
regression. Here is what I'm doing:
LOGISTIC REGRESSION VAR=group
/METHOD=ENTER v1 v2
/METHOD=ENTER v3
/CONTRAST (v3)=Helmert
/CRITERIA PIN(.05) POUT(.10) ITERATE(20) CUT(.5) .
execute.
Correct?
Ok, now for my interpretation questions:
1) Under "Omnibus tests of Model Coefficients" for Block 2, I'm
looking at the Chi-Square Step/Model values (both the same in this case) and
associated p value to assess the statistical significance of the
incremental contribution of v3. Correct?
2) I'm aware that Naglekerke's R-squared is a "pseudo"
R-squared. Can I subtract the Naglekerke R-squared value for the model
summary in Block 1 from the value in Block 2 to assess the extra variance
accounted for by v3? I'm looking for something analogous to "R-squared
change" in a hierarchical linear regression.
Thanks in advance!!!!!!
Rick
Rich Ulrich
>
> I'm a newbie to logistic regression and I have a few questions for a study
> that I'm working on. Any input would be greatly appreciated!
>
> Normally I've run analyses for hierarchical regression with a continuous
> dependent variable like this:
>
> Note - v1, v2, and group are continuous; v3 is a dichotomous dummy variable
>
>
> regression variables = v1 v2 v3 group
> /dependent=group
> /method=enter v1 v2
> /method = enter v3.
> execute.
>
> I've assessed the incremental contribution of v3 by investigating the F
> change and significance of F change and reporting the extra variance
> accounted for (R-squared change).
In OLS, the F-test for "incremental change" for the last,
single variable (1 degree of freedom) is exactly
the same test as you see for the coefficient -- whether
the test on the coefficient is expressed as the t-test
or as a one-d.f. F test.
>
> Now I'm working on an analysis where v1 and v2 are continuous, v3 is a
> dichotomous dummy variable, and group is a dichotomous variable. First, I'd
> like to check if my syntax is correct for a hierarchical logistic
> regression. Here is what I'm doing:
>
> LOGISTIC REGRESSION VAR=group
> /METHOD=ENTER v1 v2
> /METHOD=ENTER v3
> /CONTRAST (v3)=Helmert
> /CRITERIA PIN(.05) POUT(.10) ITERATE(20) CUT(.5) .
> execute.
>
> Correct?
- probably -
> Ok, now for my interpretation questions:
>
> 1) Under "Omnibus tests of Model Coefficients" for Block 2, I'm
> looking at the Chi-Square Step/Model values (both the same in this case) and
> associated p value to assess the statistical significance of the
> incremental contribution of v3. Correct?
- That sounds right -
> 2) I'm aware that Naglekerke's R-squared is a "pseudo"
> R-squared. Can I subtract the Naglekerke R-squared value for the model
> summary in Block 1 from the value in Block 2 to assess the extra variance
> accounted for by v3? I'm looking for something analogous to "R-squared
> change" in a hierarchical linear regression.
What you just pointed to in (1), is what is analogous.
The likelihood in ML improves with every added d.f., just
as the R-squared improves in OLS. The "incremental
contribution" is in terms of the log-likelihood, and
the test is that chi-squared.
There is also a test available as the ratio of the coefficient
to its standard error, testing it as the last thing-entered, just
as in OLS. Unlike what happens in OLS, this is not perfectly
identical to the test on the "contribution".
Although the ratio test is a bit less robust, it is available for
a couple of reasons-- it is easy to get, and it is available
without nearly as much extra computation (which matters
more for larger models; and in olden days). Normally the
two will be hardly differ, and either is sufficient for screening.
As always, one advantage from seeing two variations of
a test is for the implicit warning, when results vary.
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
Rick Handel
"Rich Ulrich" <wpi...@pitt.edu> wrote in message
news:khd2bv0v7b55eljht...@4ax.com...
Rick Handel
proportional improvement in the chi-square measure (McFadden's pseudo
R-squared?) in an SPSS example as follows: -2LL initial = 601.38073 and -2LL
after 4 independent variables have been included is 544.830. Therefore,
(601.38-544.83)/601.38 = .094 or 9.4%.
For my hierarchical LR example below, could I report the proportional
improvement in chi-square between blocks 1 and 2 as ((-2LLblock1) - (-2LL
block2))/-2LLblock1 as something roughly analogous to R^2 change in OLS
regression? This is what I'm interested in rather than the improvement
between block 0 and 1.
If:
> > 1) Under "Omnibus tests of Model Coefficients" for Block 2,
I'm
> > looking at the Chi-Square Step/Model values (both the same in this case)
and
> > associated p value to assess the statistical significance of the
> > incremental contribution of v3. Correct?
is analogous to R-squared change, would it appropriate to report results in
terms of proportional improvement in chi-square? (In addition to reporting
other relevant indexes too, of course).
"Rich Ulrich" <wpi...@pitt.edu> wrote in message
news:khd2bv0v7b55eljht...@4ax.com...
Rich Ulrich
On Sun, 04 May 2003 02:44:35 GMT, "Rick Handel" <bl...@no.spam> wrote:
> Next question: In Pampel's "Logistic Regression: A Primer", he reports the
> proportional improvement in the chi-square measure (McFadden's pseudo
> R-squared?) in an SPSS example as follows: -2LL initial = 601.38073 and -2LL
> after 4 independent variables have been included is 544.830. Therefore,
> (601.38-544.83)/601.38 = .094 or 9.4%.
>
> For my hierarchical LR example below, could I report the proportional
> improvement in chi-square between blocks 1 and 2 as ((-2LLblock1) - (-2LL
> block2))/-2LLblock1 as something roughly analogous to R^2 change in OLS
> regression? This is what I'm interested in rather than the improvement
> between block 0 and 1.
> [ snip, rest]
It sounds *logical* enough to me that you could do
that and cite Pampel for precedent. I wouldn't. If I were
reviewing a paper, I suspect that I would try to discourage it,
unless you have two similar situations and that helps
a convenient comparison.
Maybe I would feel otherwise if I read Pampel, but I
had not heard that folks have settled happily
on any version of "variance-accounted-for"
for ML logistic regression. And I thought that there
were intrinsic problems, such as, lacking a zero-point.
And then, instead of having a never-achieved top
like R-squared of 1.0, 100% separation in ML *does*
occur while there are still degrees of freedom left; and
it represents a degenerated model, with over-fitting.
Rick Handel
most important indexes to report for a hierarchical logistic regression? If
it's not too much trouble, how would you set up a table for the hypothetical
example I outlined below? Tomorrow, I'm going to pull several articles that
have used hierarchical LR to see how the results are usually being reported.
Unfortunately, I'm running several analyses so overall manuscript length is
going to be a concern.
"Rich Ulrich" <wpi...@pitt.edu> wrote in message
news:bq4bbvkfrqjbououg...@4ax.com...
Michael Lacy
> Thanks again for your extremely helpful replies! What do you think are the
> most important indexes to report for a hierarchical logistic regression? If
....snip.
There is a recent article reviewing various pseudo-R^2 measures for logistic
regression, and it might be of use in deciding what you might like to do. It is
more up to date and more comprehensive than the discussion in Pampel, I suspect.
DeMaris, A. 2002. "Explained Variance in Logistic Regression: A Monte Carlo Study of
Proposed Measures." Sociological Methods and Research. 31, 27-74.
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